Afraid that my cat might have swallowed a round push pin

Yesterday night, my pin board detached itself from the wall and some pins fell on the ground while my cat and I were in the room. I quickly placed the cat outside the room and closed the door to search for pins and clear the floor for my cat's safety. I think that there's one more pin to be found but I cannot find it and I've searched for it in every nook and cranny and even vacuumed the floor. I'm afraid that the remaining pin might have ricochet to outside the room since the door was open when it happened and that my cat swallowed it while he waited for me to open the door. Am I overreacting? My parent's say that my cat is too smart to swallow a sharp object and if he did swallow one, he would have been vomiting or there would be blood with his feces. My cat is acting normal, he eats and poops, doesn't appear to be in pain and runs after his toys but I've read that some symptoms appear later. My parents won't pay for vet bills since they think it would be a waste of money since there's nothing visibly wrong with him, but would pay for x-rays and surgery if there was. I don't want to wait for symptoms to show up, what if it would be too late?

Also, these are how the pins look like:


They're not as sharp as needles but can still puncture the tissue of his organs, I think.

You can always take your cat to the vet for an X-Ray to determine if he did swallow the pin or not.

You also have the option to just continue monitoring as you are; but, getting the cat to the vet quickly if you notice anything concerning.

I have heard (from my vet) about cats passing sewing needles/pins, safety pins and the like without complications. Cats have also gotten pins stick at the back of their tongues (this needed vet intervention.)

Nope, not overreacting at all

Not all cats are smart. My Aby will eat anything that fits in his mouth, whether edible or not Dust bunnies, bottle caps, paper clips, etc have made their way into his mouth and crunched on and fortunately have removed by me before they went any further.

There may not be any visible symptoms of a push pin causing problems right now but internally there could be, like a slow bleed from the pin part poking through the intestine wall. To be safe, have the vet do an x ray. The vet bill now is nothing compared to what it could be if the your cat winds up in the vet ER needing emergency surgery and treatment.

I would definitely get a x-ray, it is like that if there are symptoms it could too late. A perforated intestine will likely kill the cat. X-rays are not too expensive, and well worth the peace of mind. Please let us know how your cat is doing   

That's the thing, my parents don't want to pay for an x-ray because the cat is acting normal. The only thing that I can do is cry and beg my parents until they accept to pay for one. If there was internal bleeding, shouldn't my cat act as if he was in pain? He is still purring and very energetic, it's like nothing bad is happening to him. I hate that we have no insurance for pets. An X-ray is not that expensive, but I don't have enough money saved for it so I can pay for it on my own.

how is kitty?